Following the death of Kurt Cobain and the demise of Nirvana in 1994, Dave Grohl, the band's drummer, immediately launched a new group, the Foo Fighters, featuring himself as frontman. Derided at first, the band have now punched their way to the top

Dave Grohl bounds into the bar of the Metropolitan hotel on Park Lane and gives me a huge hug. He's half an hour late. "Oh, man, I'm so sorry. I was out shopping with my mom and I completely lost track of time." You were what? "Yeah, it's her birthday so I thought I'd treat her." Grohl's trademark goofy grin breaks over his chiselled, handsome features. For the former drummer of Nirvana and now the frontman of one of the world's biggest contemporary hard rock bands, the Foo Fighters, to be taking his mother on tour is about as rock'n'roll as admitting to a fondness for crown green bowls.

But Grohl, 33, does not in any way conform to what is expected of a rock star. He never has. His mother, Virginia, used to join him on tour with Nirvana, too. "Yeah, I guess it's not what you would call 'cool'. But, heck, who cares?"

Grohl's in a position to be so insouciant. The Foo Fighters' fourth album, One by One, hurtled straight into the UK album charts at number one and debuted in the American Top Ten at number three. After eight years of being a moderately successful band, the Foo Fighters are suddenly huge. Everyone who saw their incredible performance at Reading, headlining the Saturday of the Carling Weekend in August, agreed that something had changed. It wasn't just the fashion with which the band soared above bands such as the Strokes and the Prodigy, it was the reaction of the crowd; pure adoration was heaped on to them. Grohl admits that it was an important concert: "We'd never been so nervous before a show. I had to give a pep talk before we went on stage."

After a period of professional and personal upheaval, Grohl seems settled. Now, he's happy and relaxed and, in One by One, the Foo Fighters have made their third consecutive terrific album, following The Colour and the Shape and 1999's There Is Nothing Left to Lose. But it is a stability for which Grohl has struggled.

In the fall-out from Kurt Cobain's suicide in 1994, Grohl's decision to form the Foo Fighters (Foo Fighters was the name given by American bomber pilots to unidentified fireballs spotted over Germany during the Second World War), essentially then a solo project, was greeted with suspicion by many, a wariness that seemed justified when his half-baked debut album was released.

The album lacked focus and, crucially, memorable songs. However, 1997's The Colour and the Shape blew any doubts away. The album seethed with pain, anger and regret, and featured some excellent songs to boot. Walking Back to You even appeared on the soundtrack to BBC Two's This Life.

But if Nirvana acolytes initially thought that Grohl was railing against Cobain's death, they were ultimately disappointed. The album had been recorded in the midst of Grohl's painful divorce from his wife, Jennifer Youngblood. "That was an awful time," he grimaces, then brightens quickly, "But I'm glad you liked the record." His reputation as grunge's Paul McCartney is well-deserved; Dave Grohl is a very sunny character.

Grohl was born in Ohio, but grew up in Springfield, Virginia, a suburb of Washington DC, the son (he has an older sister, Lisa) of James and Virginia, a journalist and English teacher. His father was a speechwriter for Republican politicians ("Imagine the lectures I'd get if I fucked up, I'd get the State of the Union address!"), but also a disciplined flautist. "He thought that unless you practiced for six hours a day, you couldn't call yourself a musician; that work ethic had a big effect on me," Grohl says.

Grohl's first musical jolt, like many of his generation, came from the television show Saturday Night Live. "The B-52s played Rock Lobster on one show I was watching in 1979 - they totally blew my mind. Then, my cousin Tracy, who lived in Chicago, entered the story. She was totally punk and one summer - I was 12 or 13 - she took me to see my first live band, Naked Raygun, who were great. I stood there and thought, 'I could do this, I can play drums, and you don't even have to sing - you can just scream your balls off.' And so I just dived into the whole punk rock thing."

At 17, Grohl joined Washington's premier hardcore outfit, Scream. "My parents were a little freaked out at first; my mother because I dropped out of high school, my father because, well, because he was a Republican speechwriter. Once I started earning more money than him, though, he accepted it. Now he sits back in his chair at home, with his Scotch, and conducts our records with his baton." Grohl breaks into giggles. "He's so into the Foo Fighters now that he tried to come up with a correlation between The Colour and the Shape and West Side Story - and it almost made sense!"

Grohl was with Scream until 1990, when Krist Novoselic, Nirvana's bassist, called him and asked him to join the band. "They'd seen me play and thought I was good; Scream were disintegrating, so I thought, 'Why not?' I went on to have a pretty amazing time."

When I ask him if he still thinks of Cobain, the Mr Sunny demeanour is eclipsed. "Yeah, I think of him most days. He was my friend. It's impossible to replace a man like that." But the clouds pass swiftly when Grohl discusses Cobain's influence on his songwriting with the Foo Fighters. "He made it so simple," Grohl enthuses. "Before I joined Nirvana, all the songs I wrote were fast-fast-fast intricate punk rock. Suddenly Kurt's straightforward verse-chorus-verse song structures and understanding of dynamics made everything so clear."

I probe him about the exact nature of his and Novoselic's relationships with Cobain - were they the straight men to the singer's excesses? - but he refuses to be drawn on their intimacies and says that he feels people have dwelt too much on the dark side of the band. Certainly, it seems that Grohl never got mixed up with hard drugs, and his eminently stable background equipped him far better for rock'n'roll stardom than Kurt Cobain's fractured early years.

After Cobain's death, Grohl toyed with giving up music, but found he was still obsessed. "I'd had a great time with Nirvana and music was my life. I just couldn't give it up." He was, however, nervous about being in the spotlight. "I was frightened about fronting my own band, and once I'd teamed up with a band to tour the first record and make the second it was even worse. We had to become a band in public; journalists and fans watched our every move. It made it difficult; I guess that's why there have been so many line-up changes." (The current formation, featuring Chris Shiflett on guitar, Nate Mendel on bass and Taylor Hawkins on drums is the fourth Foo Fighters' line-up, but has been together since 1997.) Once again, his face darkens as he recalls the vituperation he faced from Nirvana fans within the media. "I still think a lot of people were like, 'How dare you come out with your own record after the death of your friend?' But, really, how dare they tell me I can't continue? I'm more precious about Nirvana than any of them."

Grohl's contribution to Nirvana was questioned recently by Cobain's widow, Courtney Love, who claimed that Grohl and Novoselic were not creatively important to Nirvana, and attempted to halt their efforts to release a greatest hits album. With the legal wrangles over, Grohl admitted that Love's typically melodramatic and unpleasant accusations had hurt.

"It didn't make me feel good, but it's one of those things. Now the lawsuit is settled, Courtney Love is getting a lot of money and we can release the album with the new song (You Know You're Right, recorded shortly before Cobain's death)."

Given Grohl's easy-going nature it is a little surprising that he regards questions about his love life as out of bounds. Since his divorce from Youngblood he's rumoured to have been involved with Louise Post from the defunct post-grunge band Veruca Salt, Winona Ryder and ex-Hole member Melissa auf der Maur, among others. But Grohl deflects any questions on the subject.

Later that day after a secret show in London I venture backstage. "Hey, Paul," Grohl says, his arm draped around a beautiful blonde, "good to see you man. This is Jordan." "A-ha," I think, "I've got you." But Grohl, as ever, has the last laugh. He looks past me and smiles. "And Paul, meet my mom." Virginia appears and shakes my hand. "Mom," Grohl laughs, "maybe you shouldn't be here. Paul doesn't think it's very rock'n'roll for you to hang out with us."